current, resistance and dc circuitsjdudek/phys112n_materials/3... · 2012-04-15 · electromotive...
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physics 112N
current, resistance and dc circuits
physics 112N 2
current! previously we considered electrostatic situations in which no E-field could exist inside a conductor
! now we move to the case where an electric field is maintained within a conductor by an external source and the conductor forms a complete circuit
! this electric field applies a force to charges within the conductor
electrical currentCoulombs/second = Amperes
physics 112N 3
current
! rate of flow of charge is uniform throughout a conductor, else charge would accumulate in certain areas
! at non-zero temperature, electrons in a metal move a lot without any applied field
! although the drift velocity of electrons is rather slow ~ 10-4 m/s, the electric fields propagate through the metal at close to the speed of light, so we never notice a delay when ‘switching on’
physics 112N 4
current
physics 112N 5
current
! what determines how much current we get for a given applied electric field or potential difference ?
! properties of the conductor determine the “resistance”
physics 112N 6
Ohm’s law
! what determines how much current we get for a given applied electric field or potential difference ?
! properties of the conductor determine the “resistance”
! (conventional) current flows from a point of high potential to a point of lower potential along the direction of the E-field
! the current is proportional to the drift velocity of the charges in the conductor
! in experiments, for many materials over a range of temperature, the drift velocity is approximately proportional to the electric field magnitude E and hence to the potential difference V
! from this follows the empirical Ohm’s law
with R a constant
resistance, R, measured in Ohms, ! = V/Aif you like mysteries think about
whether this agrees with F=ma
physics 112N 7
resistance of a wire
! we find that the resistance of a cylindrical ‘wire’
! increases with increasing length of wire (charge has further to “push through”)
! decreases with increasing cross-sectional area of wire (charge has more possible paths through the wire)
! depends upon the material the wire is made of
ρ is the resistivity which is a property of the material at a given temperature
physics 112N 11
electromotive forcecurrent will always ‘flow’ from high potential to lower potential - along the direction of the electric field
24 V
0 V
24 V
0 V
if we want a complete circuit with resistance we will need a device in which current can flow from lower to higher potential against the direction of the electric field
24 V
0 V
24 V
0 V
?
physics 112N 12
electromotive force
24 V
0 V
24 V
0 V
?
this is called an “electromotive force”examples include batteries, electric generators, solar cells, thermocouples …
ideal emf sources maintain a constant potential difference between the terminals
the device uses a force other than to move charges from low to high potential
physics 112N 14
real emf sources
! real sources of emf have an internal resistance experienced by the current as it flows through the source.
we denote this by a lower case r
! hence the potential difference between the terminals is reduced and depends upon the current flowing
! so connected in a circuit with a resistor we have
+
!
batt
ery
=
physics 112N 15
dimming bulb
As a flashlight battery ages its emf stays approximately constant, but its internal resistance increases. A fresh battery has an emf of 2.5 V and negligible internal resistance. When the battery needs replacing its emf is still 2.5 V but its internal resistance has increased to 1000 !. If this old battery is supplying 0.5 mA of current, what is its terminal voltage?
+
!
batt
ery
=
physics 112N 16
potential in a circuit - an analogy
a little like water flowing downhill ?
the emf is like the pump that gets the water to the top of the hill
physics 112N 17
measurement, voltmeters and ammeters
it’s handy to define idealised measurement tools
! ideal voltmeter draws no current (infinite resistance)
! ideal ammeter causes no change in potential (zero resistance)
V
A
physics 112N 18
power in electrical circuits
see the textbook for a derivation that shows the power transferred into a circuit element is
suppose the circuit element is a resistor
then Ohm’s law holds
so then
is the power lost from the circuit (as heat)
physics 112N 19
power in electrical circuits
see the textbook for a derivation that shows the power transferred into a circuit element is
suppose the circuit element is an ideal emf source
negative indicates that power is transferred out of the circuit element
physics 112N 24
resistors in series
Consider three resistors connected in series (part of a larger circuit)
=
⎫⎬|
⎭|
physics 112N 27
resistors in parallel
Consider three resistors connected in parallel (part of a larger circuit)
=
physics 112N 28
an example
find the current through each resistor
physics 112N 30
bulbs are resistors
! bulbs act like resistors - power loss is through heat and light
! their brightness is proportional to the power loss in them, I2R = V2/R
! so the larger the current, the brighter the bulb(or, the larger the potential drop, the brighter the bulb)
physics 112N 43
Kirchhoff’s rules! some circuits can’t be expressed in terms of parallel and series set-ups
! Kirchhoff’s rules let us deal with these
! just things we already know
! junction rule
“current into a junction = current out of a junction”
“no current is lost in a junction”
the algebraic sum of the currents into a junction is zero
physics 112N 44
Kirchhoff’s rules! some circuits can’t be expressed in terms of parallel and series set-ups
! Kirchhoff’s rules let us deal with these
! just things we already know
! loop rulethe algebraic sum of the potential difference in any loop must equal zero
aroundloop
sign conventions
physics 112N 45
Kirchhoff’s rules - example! just do a simple example to see how it works
! find the current in the circuit
physics 112N 46
Kirchhoff’s rules - example! just do a simple example to see how it works
! find the current in the circuit
! choose a direction for the current - doesn’t matter if we’re wrong, we’ll just get a negative value for I
! choose whether to go around the loop clockwise or counterclockwise - shouldn’t change the result
physics 112N 47
Kirchhoff’s rules - example! just do a simple example to see how it works
! find the current in the circuit
so we guessed the current direction wrongly
physics 112N 48
Kirchhoff’s rules - example! a more challenging example that uses both rules
! find the unknown emf, , and the current in the leftmost resistor
physics 112N 49
Kirchhoff’s rules - example! a more challenging example that uses both rules
! find the unknown emf, , and the current in the leftmost resistor
physics 112N 50
SI units summary
charge in Coulombs, C
current in Amperes, A = C/s
potential in Volts, V
energy in Joules, J = C V
power in Watts, W = J/s
resistance in Ohms, ! = V/A
* actually the ‘base’ unit (along with m, kg, s)